In-plane Vibrations of Classical Planar Frame Structures - an Exact Wave-based Analytical Solution

In this paper, classical theories are applied in modeling in-plane vibrations in planar frame structures. An exact analytical solution has been obtained using a wave vibration approach, in which vibrations are described as waves that propagate along a uniform structural element (waveguide) and are reflected and transmitted at discontinuities (such as structural joints). The propagation, reflection, and transmission matrices, as well as the matrix relations between the injected waves and externally applied forces and moments are obtained using classical vibration theories. The coupling effect between bending and longitudinal vibrations is considered in the derivations. Assembling these matrices provides a concise and systematic approach to vibration analysis of complex in-plane coupled bending and longitudinal vibrations of planar frame structures. Numerical examples are presented, with comparisons to results available in the literature.